Wavelet Shrinkage Research Articles

Application of a Novel Wavelet Shrinkage Scheme to Partial Discharge Signal Denoising of Large Generators

Partial Discharge (PD) measurements of large generators are extremely affected and hampered by noise, making the denoising of PD signal an inevitable issue. Wavelet shrinkage is the most commonly employed method for PD signal denoising. The appropriate mother wavelet and decomposition level are critically important for the denoising performance. In consideration of the PD signal characteristics of large generators, a novel wavelet shrinkage scheme for PD signal denoising is presented. In the scheme, a scale dependent wavelet selection method is proposed; the core idea is that the optimum wavelet at each scale is selected as the one maximizing the energy ratio of coefficients beside and inside the range formed by the threshold, which correspond to the signal to be reserved and noise to be removed, respectively. In addition, taking into account the influence of mother wavelet at each scale on the decomposition level, an approach for decomposition level determination is put forward based on the energy composition after decomposition at each scale. The application results on the simulated signals with different SNR obtained by combining the various pulses and measured signal on-site show the effectiveness of the proposed scheme. Besides, the denoising results are compared with that of the existing wavelet selection methods and the proposed wavelet selection method shows an obvious advantage.

MRI denoising using BM3D equipped with noise invalidation denoising technique and VST for improved contrast

Denoising of medical scanned images such as X-ray, MRI etc. is important stage in the medical use. To remove the noise from “magnetic resonance images” (MRI) is the attention of researchers to generate the MR images with high “signal-to-noise ratio” as well as with high spatial resolution. In this denoising technique, block-matching and 3-dimensional filtering (BM3D) method is used to denoise the MR images. Main steps used in BM3D are grouping, 3-dimensional discrete wavelet transformation and wavelet shrinkage. In the proposed method, noise invalidation denoising technique (NIDe) is used rather than hard thresholding. NIDe gives the threshold value automatically based on the data and noise characteristics and threshold value changes according to the characteristics of data i.e. wavelet coefficient of image. Before denoising MR images, variance stabilization transform (VST) discard the noise variance dependency of the MRI intensities. Combining block-matching and 3-dimensional filtering technique and VST make able the use of the BM3D technique for Magnetic Resonance Image denoising. After BM3D i.e. final denoised MR image, “contrast limited adaptive histogram equalization” technique is applied to increase the contrast of MR images which are denoised. Performance metrics such as “Peak Signal to Noise ratio”, “Root Mean Square Error”, “Mutual Information”, “Edge Entropy” and “Structural Similarity Index Method” are found out for “T1 weighted”, “T2 weighted” and “PD weighted” magnetic resonance images.

Soft Autoencoder and Its Wavelet Adaptation Interpretation

Recently, deep learning becomes the main focus of machine learning research and has greatly impacted many important fields. However, deep learning is criticized for lack of interpretability. As a successful unsupervised model in deep learning, the autoencoder embraces a wide spectrum of applications, yet it suffers from the model opaqueness as well. In this article, we propose a new type of convolutional autoencoders, termed as Soft Autoencoder (Soft-AE), in which the activation functions of encoding layers are implemented with adaptable soft-thresholding units while decoding layers are realized with linear units. Consequently, Soft-AE can be naturally interpreted as a learned cascaded wavelet shrinkage system. Our denoising experiments demonstrate that Soft-AE not only is interpretable but also offers a competitive performance relative to its counterparts. Furthermore, we propose a generalized linear unit (GenLU) to make an autoencoder more adaptive in nonlinearly filtering images and data, such as denoising and deblurring.

Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images

To decrease contamination from a mixed combination of impulse and Gaussian noise on color digital images, a novel hybrid filter is proposed. The new technique is composed of two stages. A filter based on a fuzzy metric is used for the reduction of impulse noise at the first stage. At the second stage, to remove Gaussian noise, a fuzzy peer group method is applied on the image generated from the previous stage. The performance of the introduced algorithm was evaluated on standard test images employing widely used objective quality metrics. The new approach can efficiently reduce both impulse and Gaussian noise, as much as mixed noise. The proposed filtering method was compared to the state-of-the-art methodologies: adaptive nearest neighbor filter, alternating projections filter, color block-matching 3D filter, fuzzy peer group averaging filter, partition-based trimmed vector median filter, trilateral filter, fuzzy wavelet shrinkage denoising filter, graph regularization filter, iterative peer group switching vector filter, peer group method, and the fuzzy vector median method. The experiments demonstrated that the introduced noise reduction technique outperforms those state-of-the-art filters with respect to the metrics peak signal to noise ratio (PSNR), the mean absolute error (MAE), and the normalized color difference (NCD).

Iterative K-Singular Value Decomposition for Quantitative Fault Diagnosis of Bearings

Previous studies have shown that a step vibration response and an impulse vibration response are generated when a rolling element passes a fault zone on the outer or inner race. The time difference between the two fault-induced responses is referred to as the time-to-impact, which can be regarded as an indication of the fault size. However, step-impulse responses, especially step responses, are often contaminated by background noise, leading to difficult time-to-impact estimation. Therefore, an effective denoising method is required to reduce noise from step-impulse responses (especially step responses) in preparation for subsequent time-to-impact estimation. To this end, an iterative K-singular value decomposition (K-SVD) algorithm is proposed to extract fault-size-related responses. This algorithm works by iteratively alternating between a modified K-SVD algorithm and a global signal reconstruction. In the numerical and experimental studies, the iterative K-SVD algorithm, the original K-SVD algorithm, and the other two benchmark algorithms (i.e., wavelet shrinkage and spectral kurtosis) were conducted for comparative analysis. The results demonstrate that the proposed algorithm could be used as a promising signal pre-processing technique for the quantitative fault diagnosis of rolling element bearings.

Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

ABSTRACT We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, ‘shrinking’ certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by ‘trial and error’, which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the ‘Haar’ wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI.

Improved Image Denoising with the Integrated Model of Gaussian filter and Neighshrink SURE

Image denoising, being an important preprocessing stage in image processing, minimizes the noise interfering with the information content of the image. The denoising problems are addressed by various techniques starting from the Fourier transforms to wavelets. Because of the localized time frequency features and advantages of multi resolution capabilities, the wavelets have been extensively used in the denoising process. The development of algorithms for the wavelet thresholding or shrinkage strategies along with different filters have resulted in the betterment of image quality after the denoising. Even though the image denoising algorithm based on a combination of Gaussian and Bilateral filters, shows good performance but lacks in consistency with respect to the noise levels and also the type of images used. This paper discusses the advantages of NeighShrink SURE rule in developing an effective thresholding strategy, thereby proposing a improved denoising method incorporating the NeighShrink SURE rule along with combination of Gaussian filter model. The methodology employs the use of subband thresholding derived from the NeighShrink SURE rule. The outcome of the proposed method exhibits a comparatively improved performance in Peak Signal to Ratio (PSNR) and Image Quality Index (IQI) values of the test images.

Group-Based K-SVD Denoising for Bearing Fault Diagnosis

Vibration signals acquired by accelerometers are commonly used in the field of bearing fault diagnosis. The measured vibration signals contain a series of impulse responses when localized bearing faults occur. These impulses are often viewed as fault features and exhibit nonlocal self-similarity in terms of morphological characteristics. However, the impulses are generally contaminated by background noise. In this paper, a group-based K-SVD denoising algorithm, which exploits the nonlocal self-similarity property, is presented to extract bearing fault features. In contrast to regular K-SVD denoising, this denoising algorithm forms groups by clustering similar signal segments and regards each group rather than each segment as the basic unit of sparse representation. To group similar segments, we further propose a particular grouping method that exploits bearing prior knowledge (i.e., possible impulse spacings). The new grouping method could form groups in a targeted manner, thereby achieving more accurate grouping. Group-based K-SVD denoising is able to extract fault features better as similar segments collaboratively provide a large amount of shared feature information, especially in the presence of strong noise (such as signal-to-noise ratios lower than −10 dB). The numerical and experimental results demonstrate the superior performance of group-based K-SVD denoising over regular K-SVD denoising and other two benchmark algorithms (i.e., wavelet shrinkage and spectral kurtosis).

Multipatch Unbiased Distance Non-Local Adaptive Means With Wavelet Shrinkage

Many existing non-local means (NLM) methods either use Euclidean distance to measure the similarity between patches, or compute weight ωij only once and keep it unchanged during the subsequent denoising iterations, or use only the structure information of the denoised image to update weight ωij . These may lead to the limited denoising performance. To address these issues, this paper proposes the non-local adaptive means (NLAM) for image denoising. NLAM treats weight ωij as an optimization variable and iteratively updates its value. We then introduce three unbiased distances, namely, pixel-pixel, patch-patch, and coupled unbiased distances. These unbiased distances are more robust to measure the image pixel/patch similarity than Euclidean distance. Using the coupled unbiased distance, we propose the unbiased distance non-local adaptive means (UD-NLAM). Because UD-NLAM uses only a single patch size to compute weight ωij , we introduce multipatch UD-NLAM (MUD-NLAM) to adapt different noise levels. To further improve denoising performance, we then propose a new denoising method called MUD-NLAM with wavelet shrinkage (MUD-NLAM-WS). Experimental results show that the proposed NLAM, UD-NLAM, and MUD-NLAM outperform existing NLM methods, and MUD-NLAM-WS achieves a better performance than the state-of-the-art denoising methods.

Image decomposition using a second-order variational model and wavelet shrinkage

The paper is devoted to the new model for image decomposition, that splits an image $f$ into three components $u+v+\omega$, with $u$ a piecewise-smooth or the ``cartoon'' component, $v$ a texture component and $\omega$ the noise part in variational approach. This decomposition model is in fact incorporates the advantages of two preceding models: the second-order total variation minimization of Rudin-Osher-Fatemi (ROF2), and wavelet shrinkage for oscillatory functions. This decomposition model is presented as an extension of the three components decomposition algorithm of Aujol et al. in \cite{JAC}. It also continues the idea introduced previously by authors in \cite{TPB}, for two components decomposition model. The ROF2 model was first proposed by Bergounioux et al. in \cite{BP}, it is an improved regularization method to overcome the undesirable staircasing effect. The wavelet shrinkage is well combined to separate the oscillating part due to texture from that due to noise. Experimental results validate the proposed algorithm and demonstrate that the image decomposition model presents effective and comparable performance to other state-of-the-art models.

The STNRW-ECF estimator for stable distributions with application in ECG beat

The α-stable distribution can describe a degree of concentration of the observations around the mean as well as their asymmetry, regardless of sample size. As the α stability index is the most interesting parameter in the applications, several estimators have been proposed for α. Here we develop an estimator for α (called STNRW-ECF) based on the empirical characteristic function and the Seismic Trace Noise Reduction by Wavelets and Double Threshold Estimation method (STNRW). We analyze the proposed estimator using Monte Carlo simulations and prove its asymptotic Gaussian distribution. Electrocardiography (ECG) is the process of recording the electrical activity of the heart over a period of time using electrodes placed on the skin. The time intervals between its various peaks, may contain useful information about the nature of disease afflicting the heart. To analyze this kind of data can be tiring and more prone to errors when interpreted by human beings, since there is a huge amount information to be processed. Here we propose the STNRW-ECF estimator to be an additional diagnostic tool that may provide an indication of cardiac arrhythmia, and we also propose a test based on the principal wavelet shrinkage to confirm whether or not the STNRW-ECF estimator should be used for this purpose.

The stationary wavelet transform as an efficient reductor of powerline interference for atrial bipolar electrograms in cardiac electrophysiology

Objective: The most relevant source of signal contamination in the cardiac electrophysiology (EP) laboratory is the ubiquitous powerline interference (PLI). To reduce this perturbation, algorithms including common fixed-bandwidth and adaptive-notch filters have been proposed. Although such methods have proven to add artificial fractionation to intra-atrial electrograms (EGMs), they are still frequently used. However, such morphological alteration can conceal the accurate interpretation of EGMs, specially to evaluate the mechanisms supporting atrial fibrillation (AF), which is the most common cardiac arrhythmia. Given the clinical relevance of AF, a novel algorithm aimed at reducing PLI on highly contaminated bipolar EGMs and, simultaneously, preserving their morphology is proposed. Approach: The method is based on the wavelet shrinkage and has been validated through customized indices on a set of synthesized EGMs to accurately quantify the achieved level of PLI reduction and signal morphology alteration. Visual validation of the algorithm’s performance has also been included for some real EGM excerpts. Main results: The method has outperformed common filtering-based and wavelet-based strategies in the analyzed scenario. Moreover, it possesses advantages such as insensitivity to amplitude and frequency variations in the PLI, and the capability of joint removal of several interferences. Significance: The use of this algorithm in routine cardiac EP studies may enable improved and truthful evaluation of AF mechanisms.

Denoising scheme based on singular-value decomposition for one-dimensional spectra and its application in precision storage-ring mass spectrometry.

This work concerns noise reduction for one-dimensional spectra in the case that the signal is corrupted by an additive white noise. The proposed method starts with mapping the noisy spectrum to a partial circulant matrix. In virtue of singular-value decomposition of the matrix, components belonging to the signal are determined by inspecting the total variations of left singular vectors. Afterwards, a smoothed spectrum is reconstructed from the low-rank approximation of the matrix consisting of the signal components only. The denoising effect of the proposed method is shown to be highly competitive among other existing nonparametric methods, including moving average, wavelet shrinkage, and total variation. Furthermore, its applicable scenarios in precision storage-ring mass spectrometry are demonstrated to be rather diverse and appealing.

K - Shrinkage Function for ECG Signal Denoising.

ECG signals is a graphical way of recording the electrical actions of the heart for the various diagnostic purposes. ECG signals are affected by various noises such as Electrode Contact, Baseline Wandering, Motion artifact, Power-line interference, Muscle Contractions, and Electrosurgical noise during data acquisition. Denoising is a technique which is used for removing the noise in ECG signals which keeps the useful information. In this paper, a new category of Wavelet shrinkage methods is proposed. The white Gaussian noise is mixed with the ECGs for simulation and tested with the new class of shrinkage function and is compared with the other wavelet shrinkage functions such as hard and soft shrinkage. The performance measures such as Signal to Noise Ratio (SNR) and Percent Root mean - square Difference (PRD) etc. are used to examine the performance of various shrinkage functions. The experimental result shows that it gives better MSE over conventional shrinkage functions.

Hybrid SAR Speckle Reduction Using Complex Wavelet Shrinkage and Non-Local PCA-Based Filtering

In this paper, a new hybrid despeckling method, based on Undecimated Dual-Tree Complex Wavelet Transform (UDT-CWT) using maximum a posteriori (MAP) estimator and non-local Principal Component Analysis (PCA)-based filtering with local pixel grouping (LPG-PCA), was proposed. To achieve a heterogeneous-adaptive speckle reduction, SAR image is classified into three classes of point targets, details, or homogeneous areas. The despeckling is done for each pixel based on its class of information. Logarithm transform was applied to the SAR image to convert the multiplicative speckle into additive noise. Our proposed method contains two principal steps. In the first step, denoising was done in the complex wavelet domain via MAP estimator. After performing UDT-CWT, the noise-free complex wavelet coefficients of the log-transformed SAR image were modeled as a two-state Gaussian mixture model. Furthermore, the additive noise in the complex wavelet domain was considered as a zero-mean Gaussian distribution. In the second step, after applying inverse UDT-CWT, an iterative LPG-PCA method was used to smooth the homogeneous areas and enhance the details. The proposed method was compared with some state-of-the-art despeckling methods. The experimental results showed that the proposed method leads to a better speckle reduction in homogeneous areas while preserving details.

Domain-independent severely noisy image segmentation via adaptive wavelet shrinkage using particle swarm optimization and fuzzy C-means

Noisy image segmentation is a hot topic in natural, medical, and remote sensing image processing. It is among the non-trivial problems of computer vision having to address denoising and segmentation at the same time. Fuzzy C-means (FCM) is a clustering algorithm that has been shown to be effective at dealing with both segmentation-oriented denoising and segmentation at the same time. Moreover, with a high level of noise and other imaging artifacts, FCM loses its ability to perform image segmentation effectively. This paper introduces a Particle Swarm Optimization (PSO)-based feature enhancement approach in the wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using FCM clustering performance as an evaluation mechanism and also as the segmentation algorithm. The PSO-based process helps to enhance intensity features for clustering-based denoising, and also provides adaptivity for the system that performs well on a range of real, synthetic, and simulated noisy images with different noise levels and range/spatial properties. Furthermore, the algorithm applies edge enhancement based on Canny edge detector in order to further improve accuracy. Experiments are presented using three different datasets each degraded with different types of common noise. The presented algorithms show effective and consistent performance over a range of severe noise levels without the need for any parameter tuning.

A novel algorithm for crack path identification based on infrared images

The present work aims at developing a new approach towards the analysis of the crack path through the access to the information from the infrared (IR) video imaging of the steady fatigue crack growth. We first test some commonly available infrared image filtering techniques, and then we introduce a new robust algorithm to identify the position of the dynamic crack. The proposed procedure performs the local analysis of the temperature distribution around the fatigue crack tip in the 316L stainless steel. The developed MATLAB framework simplifies the routine processing and permits analyzing multiple experiments reasonably easily. Two filtering procedures - Gaussian and wavelet shrinkage - were implemented and applied successively to denoise the IR images. Both filters produce comparable and good quality results. The new algorithm capable of automatic locating the crack tip position from consecutive filtered IR images is proposed. Remarkably successful results are demonstrated with only small errors caused by materials distortion.

SAR Image Denoising Algorithm Based on Bayes Wavelet Shrinkage and Fast Guided Filter

To remove the speckle noise of synthetic aperture radar (SAR) images, a novel denoising algorithm based on Bayes wavelet shrinkage and a fast guided filter is proposed. According to the statistical properties of SAR images, the noise-free signal and speckle noise in the wavelet domain are modeled as Laplace and Fisher-Tippett distributions respectively. Then a new wavelet shrinkage algorithm is obtained by adopting the Bayes maximum a posteriori estimation. Speckle noise in the high-frequency domain of SAR images is shrunk by this new wavelet shrinkage algorithm. As the wavelet coefficients of the low-frequency domain also contain some speckle noise, speckle noise in the low-frequency domain can be further filtered by the fast guided filter. The result of the denoising experiments of simulated SAR images and real SAR images demonstrate that the proposed algorithm has the ability to better denoise and preserve edge information.

A wavelet and adaptive threshold-based contrast enhancement of masses in mammograms for visual screening

The screening of mammograms is a difficult task for the radiologist, due to variation in contrast and homogeneous structure of the masses and surrounding breast tissues. Therefore, an adaptive threshold-based contrast enhancement method is proposed in this paper for enhancement of suspicious masses in mammograms. Homomorphic filtering and wavelet-based denosing has been used prior to enhancement in the describe method. The approach contains, artefact suppression using pre-processing. Then wavelet transform is applied on the preprocessed mammogram, homomorphic filter is used to filter the approximate coefficient and wavelet shrinkage operator is applied on detail coefficients for denoising. Finally, contrast enhancement approach is used to enhance the suspicious region based on adaptive threshold technique. Two databases, namely Digital Database for Screening Mammography (DDSM) and Mammographic Image Analysis Society (MIAS), were used to test proposed method. The obtain results using proposed method gives better visibility for suspicious masses for all types of mammograms.

Novel Method for Lung Tumour Detection Using Wavelet Shrinkage-based Double Classifier Analysis

Medical image detection and classification play an important role in medical research. Tumour detection is a process of crucial importance in oncology. The aim of this paper is to devise an approach for efficient image enhancement, tumour detection, and classification on computed tomographic lung images. Three different application-related methods on computed tomography (CT) images have been designed and implemented in this work. The first method, which was based on image quality, enhances the performance of the medical images. Generally, the CT images are very sensitive to noise and are difficult to handle. Proper care may be taken by introducing some preprocessing algorithms like enhancement algorithms and filters. According to this, an image enhancement algorithm, Wavelet Shrinkage adaptive histogram Equalization (WSAHE), with anisotropic diffusion filter (ADF) was introduced to improve the contrast of the CT images and denoising. In the second method Seed Region growing with Random walk segmentation algorithm (SRGWRWS) is proposed for lung tumour segmentation. In the third method GLCM features, FOS features, structural features, and combinational features are calculated from the segmented lung images. After segmentation, the tumour classification is done by Multi-class support vector machine (MCSVM) and Descend RUSBOOST classifiers. Here, MCSVM classifier was used to find whether the input CT tumour image is suspicious, benign or malignant. Overall accuracy of 92% is obtained using Descend RUSBOOST classifier with GLCM features, FOS features, structural features, combinational features and overall accuracy of 97% is obtained using MCSVM classifier with GLCM feature in MATLAB 2017a software.